We just got a kitten who seems to have allergies, runny nose, icky eyes. I know dogs can take Benadryl, can cats? And what dosage would I give, she's only 10-12 weeks old?

I would not give her anything without taking her to a vet.

Sounds like she has some kind of infection

Hello harrisshirley84,
According to my knowledge she has effected by some kinds of infection
So I will suggest that you take the advice your animal doctor.because he will be well understand your cat infection.

The first thing that you need to learn is that cats have very different physiology from humans and dogs, and it's really unsafe to give them medications without running it past the vet. Drugs that are perfectly safe for humans and dogs can kill your cat.

Second, this sounds like a URI (upper respiratory tract infection... i.e.. a cold). They tend to be common in kittens that have just been adopted. Vets are used to seeing them, and can give you the antibiotics that you need to clear it up.